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Technical Note—A Note on Shot-Noise and Reliability Modeling

Author

Listed:
  • Austin J. Lemoine

    (Ford Aerospace & Communications Corporation, Palo Alto, California)

  • Michael L. Wenocur

    (Ford Aerospace & Communications Corporation, Palo Alto, California)

Abstract

We discuss a reliability model that reflects the dynamic dependency between system failure and system stress. For example, the mortality rate for individuals who have had a heart attack declines with time. In particular, we use a shot-noise process to model “residual system stress,” which in turn drives a doubly stochastic Poisson process model for system failures. Intuitively, residual stress (or susceptibility to failure) may vary in a random manner yet be essentially unobservable, while system failures may be readily detectable and observable. Shot-noise distributions have a richness and subtlety that suggest untapped potential for applications. The doubly stochastic Poisson process provides a reasonable framework for modeling randomly varying rates of occurrence in a broad variety of settings.

Suggested Citation

  • Austin J. Lemoine & Michael L. Wenocur, 1986. "Technical Note—A Note on Shot-Noise and Reliability Modeling," Operations Research, INFORMS, vol. 34(2), pages 320-323, April.
    • Handle: RePEc:inm:oropre:v:34:y:1986:i:2:p:320-323
    DOI: 10.1287/opre.34.2.320
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    Citations

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    Cited by:

    1. Cha, Ji Hwan & Finkelstein, Maxim, 2018. "On information-based residual lifetime in survival models with delayed failures," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 209-216.
    2. Laskin, Nick, 2018. "Valuing options in shot noise market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 518-533.
    3. Cha, Ji Hwan & Finkelstein, Maxim, 2016. "On some properties of shock processes in a ‘natural’ scale," Reliability Engineering and System Safety, Elsevier, vol. 145(C), pages 104-110.
    4. Qiu, Qingan & Cui, Lirong, 2019. "Optimal mission abort policy for systems subject to random shocks based on virtual age process," Reliability Engineering and System Safety, Elsevier, vol. 189(C), pages 11-20.
    5. van Noortwijk, J.M., 2009. "A survey of the application of gamma processes in maintenance," Reliability Engineering and System Safety, Elsevier, vol. 94(1), pages 2-21.
    6. Ji Cha & Maxim Finkelstein & Francois Marais, 2014. "Survival of systems with protection subject to two types of external attacks," Annals of Operations Research, Springer, vol. 212(1), pages 79-91, January.

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